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Manager  Joined: 02 Dec 2012
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On the number line above, p, q, r, s, and t are five consec  [#permalink]

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Question Stats: 82% (01:26) correct 18% (01:43) wrong based on 1746 sessions

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On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers?

(1) q + s =24
(2) The average (arithmetic mean) of q and r is 11.
Math Expert V
Joined: 02 Sep 2009
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Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

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6 On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers?

{p, q, r, s, t} is an evenly spaced set thus its mean = median = middle term = r.

(1) q + s =24. Since q, r and s are consecutive even integers, then q=r-2 and s=r+2 --> (r-2)+(r+2)=24 --> r=12. Sufficient.

(2) The average (arithmetic mean) of q and r is 11. (r-2)+r=2*11 --> r=12. Sufficient.

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Intern  Joined: 12 Nov 2012
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Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

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which is the level of the question? 500? tks a lot Math Expert V
Joined: 02 Sep 2009
Posts: 65785
Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

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fabrizio1983 wrote:
which is the level of the question? 500? tks a lot I'd say it's ~600.

P.S. You can see the difficulty level of a question in the first post where the tags are (TAGS: Difficulty: 600-700 Level).
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Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

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Attachment:
Number line.png
On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers?

(1) q + s =24
(2) The average (arithmetic mean) of q and r is 11.

Ans. : Let p=x, q=x+2, r=x+4 , s=x+6, t=x+8 to find the mean we need to find x.
From statement 1 , we get 2x+8=24
From statement 2 we get x+3=11
Intern  Joined: 06 Dec 2012
Posts: 4
Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

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My understanding of consecutive integers, is that they are separated by only 1, i.e. 3, 4, 5, 6, 7, 8

I was able to find the first statement sufficient, but not the second, mainly because the answer uses the formula p + (p+2) +....

Why is 2 being added to P?
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Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

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1
My understanding of consecutive integers, is that they are separated by only 1, i.e. 3, 4, 5, 6, 7, 8

I was able to find the first statement sufficient, but not the second, mainly because the answer uses the formula p + (p+2) +....

Why is 2 being added to P?

We are not told that p, q, r, s, and t are consecutive integers. We are given that p, q, r, s, and t are five consecutive EVEN integers. For example 2, 4, 6, 8, 10.
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Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

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They are basically giving us some equation in disguise.

1. q+s=24 but for a fact set we know that the leap between q and s is 4 and this translates into an equation that subtracted gives us the value of q from which we can calculate the average.
2. q+r=22 same old story, the leap between q and r this time is 2 units. r-q=2 subtract it from the given equation and you are done you got one value, the remaining values follow logically.

D.
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Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

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2
1
Hi All,

This DS question is full of Number Properties and the math involved is fairly straight-forward. However, if you don't see the "elegant" approach to answer this question, then you can still use "brute force" and some basic Arithmetic to get the correct answer.

We're given a number line with 5 variables on it. We're told that the variables represent 5 CONSECUTIVE EVEN INTEGERS. That's a very specific set of "restrictions", so you can use them to your advantage if you have to "play around" with this question. We're asked for the AVERAGE of the 5 integers. Since we know that they're consecutive evens, if we can figure out ANY of them, then we can figure out the others AND answer the question.

Fact 1: Q + S = 24

Looking at the drawing, we know that Q, R and S are 3 CONSECUTIVE EVEN INTEGERS, so even if we don't know how to do the Algebra here, we can still run some TESTs....

IF Q, R and S are....
2, 4 and 6, then Q+S = 8. That's too small though (it's supposed to be 24)

IF Q, R and S are a bit bigger, say....
8, 10 and 12, then Q + S = 20. This is still too small, but it's getting closer to 24...

IF Q, R and S are....
10, 12 and 14, then Q + S = 24. This is a MATCH for what we're looking for. We can also figure out the missing values (they're 8 and 16).

By making these variables larger or smaller, the sum of Q+S won't = 24, so we know that the 10/12/14 example is the ONLY possibility that fits.
Fact 1 is SUFFICIENT.

Fact 2: The average of Q and R is 11

Since Q and R are 2 CONSECUTIVE EVEN INTEGERS, we're going to need 2 numbers that are close to 11....

IF Q and R are....
8 and 10, then the average is 9 (which is not a match; it's supposed to be 11)

IF Q and R are...
10 and 12, then the average is 11. This is a MATCH.

Making Q and R any bigger will raise the average (and it won't match), so we know that 10 and 12 are the ONLY possible values that fit. The other numbers would be 8, 14 and 16.
Fact 2 is SUFFICIENT.

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On the number line above, p, q, r, s, and t are five consec  [#permalink]

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Attachment:
Number line.png
On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers?

(1) q + s =24
(2) The average (arithmetic mean) of q and r is 11.

Solution:

Recall that in a set of evenly spaced numbers, mean is equal to the median. Thus, the average of these five integers is equal to r.

Statement One Alone:

q + s = 24

Notice that the set consisting of q, r and s is also evenly spaced; therefore the mean of this set is also equal to the median, which is r. Recall that for a set of evenly spaced numbers, the mean is equal to the average of the greatest and the smallest elements; thus r = mean = (q + s)/2 = 24/2 = 12.

Statement one alone is sufficient.

Statement Two Alone:

The average of q and r is 11.

Since (q + r)/2 = 11, q + r = 22. Since q and r are consecutive even integers, q = r - 2. Then, (r - 2) + r = 2r - 2 = 22. Solving the equation, we get r = 12.

Statement two alone is sufficient.

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Originally posted by ScottTargetTestPrep on 14 May 2016, 04:56.
Last edited by ScottTargetTestPrep on 06 Mar 2020, 06:36, edited 1 time in total.
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Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

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Attachment:
Number line.png
On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers?

(1) q + s =24
(2) The average (arithmetic mean) of q and r is 11.

Given:
CONSECUTIVE EVEN INTEGERS
p=2n
q=2n+2
r=2n+4
s=2n+6
t=2n+8

p<q<r<s<t

Mean= (2n+2n+2+2n+4+2n+6+2n+8)/5
= (10n+20)/5
=10(n+2)/5
=2(n+2)

(1) q+s=24
2n+2+2n+6=24
One variable thus can be solved.

Sufficient.

(2) Mean= (2n+2+2n+4)/2

One variable thus can be solved.

D
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Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

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STatement 1 no. of terms is 5 so the center term i.e r will be the avg as the series is an Arithmetic progression
so it can be found by (q +s)/2 = 12.

Statement 2 : given :- (q + r) / 2 = 11.
also q = r-2 (as all are even consecutive integers in a series.)
So again the avg can be found out.

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Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

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1) q+s=24
p,q,r,s,t

s-q= 4 and s+q =24. add them. s=14 and series will be 8,10,12,14,16 and mean will be 12. sufficient A/D can be answer

2) mean of q and r is 11, q+r=22.
r+q=22 , r-q =2 add them r=12, and series will be again same and same answer as above therefore sufficient

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Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

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2
Attachment:
Number line.png
On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers?

(1) q + s =24

As we know that r is the median of q and s, and r is also the median of p,q,r,s, and t. Hence, if we know the value of r we should be able to answer the question.

q + s = 24

Midpoint = 24/2 = 12 = r

Hence, (1) ===== is SUFFICIENT

(2) The average (arithmetic mean) of q and r is 11

q = r - 2

r - 2 + r = 11 * 2

2r = 24

r = 12

Hence, (2) ===== is SUFFICIENT

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On the number line above, p, q, r, s, and t are five consec  [#permalink]

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Updated - Thank you for bring it up.
Thanks__

Originally posted by TheUltimateWinner on 04 Mar 2020, 02:50.
Last edited by bb on 06 Mar 2020, 07:52, edited 1 time in total.
Quote removed - thanks for bringing it up On the number line above, p, q, r, s, and t are five consec   [#permalink] 04 Mar 2020, 02:50

# On the number line above, p, q, r, s, and t are five consec  